Landslides are natural phenomena that can cause costly damage when occurring in or impacting constructed areas. Landslide risk analysis is used to estimate the risk of landslide hazard to individuals, populations, properties, or the environment (Fell et al., 2008; Corominas et al., 2014, 2015) and generally contains five main steps: (i) hazard identification, (ii) hazard assessment, (iii) inventory of elements at risk and exposure, (iv) vulnerability assessment, and (v) risk estimation. Landslide risk analysis is useful to locate the zones where the risk is highest, but it is a complex and time-consuming task, especially when the study is conducted at the municipal scale.

During the last three decades, the landslide risk (R) has been considered as the product of the landslide hazard (H), the vulnerability (V), and the value of the elements at risk (EV) (Varnes and the IAEG Commission on Landslides and other Mass-Movements, 1984; Michael-Leiba et al., 1999; Cardinali et al., 2002; Remondo et al., 2005; Uzielli et al., 2008; van Westen et al., 2008; Zêzere et al., 2008): R = H × V × EV, where R is the risk (annual loss of property value). Landslide hazard (H) is the probability of occurrence within a specified period of time and within a given area of a potentially damaging phenomenon (Varnes and the IAEG Commission on Landslides and other Mass-Movements, 1984) having a given magnitude (Jaiswal et al., 2011a), which is typically measured with the landslide area or the landslide volume (Lee and Jones, 2004; Li et al., 2010). The vulnerability (V) concept is defined in physical terms as the “degree of loss” of a given element or set of elements at risk exposed to the occurrence of a landslide of a given magnitude, expressed in a scale ranging from 0 (no loss) to 1 (total loss) (e.g. Varnes and the IAEG Commission on Landslides and other Mass-Movements, 1984; Remondo et al., 2008). The value of the elements at risk is the economic value (EV) of the elements at risk, which in this study correspond to the built environment.

Whereas the landslide susceptibility and the landslide hazard have been extensively studied in the last two decades, whether with heuristic, statistic-probabilistic, or deterministic methods (e.g. Fell et al., 2008; Corominas et al., 2014), less work has been done, for various reasons, on the spatial assessment of landslide vulnerability and on the assessment of the value of the elements at risk (e.g. Zêzere et al., 2007, 2008; Papathoma-Köhle et al., 2012a; Silva and Pereira, 2014).

First, for most types of landslide, very limited damage data are available (van Westen et al., 2005; Papathoma-Köhle et al., 2012a), which hamper the creation and validation of any reliable vulnerability model. Second, different physical mechanisms are associated with different types of landslides, which mean that the same elements at risk have different vulnerability to different types of landslides. Therefore, the method used for assessing rockfall vulnerability would not be directly transferable to the slow slide vulnerability assessment (Alexander, 2005; Papathoma-Köhle et al., 2011; Ciurean et al., 2013). Third, the vulnerability of the elements at risk depends on the landslide intensity, which is usually associated with the landslide velocity (Hungr, 1997; Lateltin et al., 2005) that may range from some millimetres per year to several metres per second (Cruden and Varnes, 1996).

Moreover, methods used to assess vulnerability should be selected according to the scope and the scale of the study, which influences the level of spatial detail requested (Papathoma-Köhle et al., 2011). A vulnerability study conducted at the municipal level typically implies the existence of a large number of elements at risk (e.g. buildings) and details about building characteristics and landslide damage. Due to this reason, landslide vulnerability assessment is usually performed in small study areas with a reduced number of exposed elements in order to ease the methodology demonstration (e.g. Uzielli et al., 2015).

Previous studies have attempted to assess the landslide vulnerability and to analyse the landslide risk. Some of them are qualitative, focusing on human lives (e.g. Santos, 2003) and in both buildings and human lives (Macquarie et al., 2004). Other physical vulnerability studies are semi-quantitative, assigning empirical weighting of a set of building resistance parameters to buildings exposed to landslides (e.g. Silva and Pereira, 2014), or applying vulnerability curves to buildings exposed to hydrometeorological hazards (e.g. Godfrey et al., 2015).

Quantitative vulnerability studies usually aim to estimate the physical vulnerability of buildings based on landslide intensity parameters (e.g. impact energy, average velocity) and resistance or susceptibility of the exposed elements (e.g. structure type, construction material, maintenance state) (e.g. Uzielli et al., 2008, 2015; Li et al., 2010; Du et al., 2013; Peng et al., 2015). Most of the time, landslide intensity parameters can be quantified (e.g. landslide velocity), while proposed values for resistance or susceptibility of the exposed buildings are usually assigned based on expert opinion (Peng et al., 2015; Uzielli et al., 2015), which may increase the subjectivity and uncertainty of the vulnerability estimation. In addition, expert surveys can be used to estimate physical vulnerability using the standard deviation of the expert answers to measure the variability of the average vulnerability (Winter et al., 2014).

Physical vulnerability assessment has several sources of uncertainty that can be either epistemic or aleatory (Ciurean et al., 2013). Epistemic uncertainties can come from the use of proxies for the landslide intensity assessment (e.g. velocity, depth of affected material, volume), or from the characterization of elements at risk (e.g. structural-morphological characteristics, state of maintenance, strategic relevance), from the vulnerability model (e.g. selection of parameters, mathematic model, calculation limitations), or from expert judgement about building resistance parameters and landslide damaging potential (Ciurean et al., 2013). Aleatory uncertainties come from the spatial variability of parameters (e.g. landslide intensities, population density) (Ciurean et al., 2013). For instance, the position of the element at risk (e.g. a building) on the track of a landslide is a source of aleatory uncertainty as the damage would not be the same if it is located on the crown of the landslide or on its run-out zone (van Westen et al., 2005).

Some examples of non-site-specific studies on landslide risk to buildings are available in the technical literature (e.g. Michael-Leiba et al., 1999; Cardinali et al., 2002; Remondo et al., 2008; Uzielli et al., 2008; Zêzere et al., 2008; Jaiswal et al., 2010, 2011b; Uzielli et al., 2015). Despite the progress already made, major limitations persist on the reliable assessment of landslide frequency and magnitude (which are both critical for the hazard assessment), and on the quantification of the buildings' vulnerability, which is frequently based on expert opinion. This work aims to contribute to the fulfilling of a research gap on the physical vulnerability assessment based on expert opinion. The main purposes of the study are to develop and apply a method for building vulnerability assessment in a Portuguese municipality (Loures), and to analyse the landslide risk to buildings in this study area.

Following the previous work of Guillard and Zêzere (2012), the susceptibility of the slopes was modelled for deep-seated and shallow slides, and the hazard was assessed, considering the magnitude probability of the landslide area and the annual and multiannual spatiotemporal probability of landslides.

In this study, there are few records on building damage caused by landslides, which constitutes a drawback in the construction and validation of the vulnerability model. Due to this reason, buildings' physical vulnerability assessment was based on expert judgment of a pool of European landslide experts. In addition, from this pool, we extracted a sub-pool constituted by experts that have been working in the study area, i.e. who have a deep knowledge of both the landslides and the built environment of the study area. With this methodology, we aimed to evaluate the variability of the expert judgments, comparing the answers from the pool of landslide European experts with the answers from the sub-pool of landslide experts who know the study area, assessing thus the epistemic uncertainty in buildings' vulnerability assessment and evaluating how vulnerability controls risk results.

The market economic value of the buildings was assessed per pixel and the buildings' landslide risk of the municipality of Loures was assessed for different spatiotemporal probabilities using pixel units in a GIS environment.

For various reasons we chose to analyse the risk of slides triggered by rainfall in the Loures municipality, near Lisbon. First, this municipality is prone to different natural hazards and in particular to landslides. Most of the landslides in the Loures municipality are rotational or translational and are triggered by rainfall (Zêzere et al., 2004, 2008). Landslides were classified according to the depth of slip surface in two groups: shallow slides (slip surface depth ≤ 1.5 m) and deep-seated slides (slip surface depth > 1.5 m). The landslide inventory includes 333 shallow slides (average area 961 m2) and 353 deep-seated slides (average area 3806 m2). Velocity of landslides is typically slow for shallow slides and very slow or extremely slow for deep-seated slides, according to Cruden and Varnes' (1996) classification. These landslides often affect buildings and roads with significant direct and indirect consequences. Out of 686 landslides (Fig. 1) inventoried by Guillard and Zêzere (2012), 462 occurred within 50 m of buildings and roads, and some of them had caused damage to a built environment in the past (Zêzere et al., 2008).

Second, Loures is adjacent to the city of Lisbon (Fig. 1), hence a large number of inhabitants, buildings, and infrastructures are exposed to landslide hazard; indeed, about 205 000 persons currently live in the Loures municipality (density around 1220 inhabitants per km2), which is 6 % higher than in 2001 according to the National Institute of Statistics (INE, 2002, 2011). The mean age of the buildings is 37.5 years, 66.9 % of them with a structure of reinforced concrete, 30.6 % of masonry, 1.8 % of adobe, rammed earth, or loose stone, and 0.7 % of other materials (INE, 2011). The 32 495 buildings of the Loures municipality represent a total built-up area of 9.25 km2 and the number of buildings, most of which were erected without taking into account the possibility of future landslide occurrence, increase every year. Indeed, according to the results obtained in the framework of the new Master Plan for the Lisbon Metropolitan Area, the construction on potentially unstable slopes within the Loures municipality increased by 64 % between 1995 and 2007.

Third, a study on the susceptibility of slopes to landslides was previously conducted in this municipality (Guillard and Zêzere, 2012). Therefore, we intend to complete the risk analysis for buildings in this study area.

Finally, a social vulnerability assessment was conducted for the greater Lisbon area (Guillard-Gonçalves et al., 2015), which opens up an avenue for a future study that combines these two dimensions of the vulnerability.

Additional information about the study area can be found in Guillard and Zêzere (2012).

The frequency–magnitude relationship of the inventoried landslides was established, plotting the probability of a landslide area. The susceptibility of deep-seated and shallow landslides was assessed by a bivariate statistical method and has been mapped. The annual and multiannual spatiotemporal probabilities were estimated, providing a landslide hazard model. Then, the physical vulnerability was assessed by analysing the answers to a questionnaire that had been sent to a pool and a sub-pool of landslide experts. The vulnerability map was based on statistical mapping units for the whole study area, and based on fieldwork building inventory for a test site included in the study area. Next, the market economic value of the buildings was calculated. Finally, the landslide risk (R) was computed by multiplying the potential loss (V × EV) by the hazard probability (H).

The vulnerability values obtained in this study are in agreement with the ones found in the literature. Indeed, we found that in general, landslides smaller than ∼ 1500 m2 resulted in negligible to significant damage to buildings, corresponding to a vulnerability of 0.6 or less, whereas landslides larger than ∼ 7000 m2 produced significant to very severe damage, corresponding to a vulnerability of 0.6 or higher, which is in agreement with the results found by Galli and Guzzetti (2007). Moreover, in terms of accumulated material height, the landslides that have a 5 m depth of accumulated material, produce an average damage for the four structural building types corresponding to a vulnerability of 0.91. For comparison, the vulnerability curves computed by Papathoma-Köhle et al. (2012b) using a Weibull distribution show that debris flows produce a total destruction (vulnerability = 1) when the accumulated material reaches 3.5 m high. Considering that the debris flows' intensity is increased by their velocity, it is understandable that their potential for damage is higher than the potential for damage of the slow landslides considered in the present study.

The answers obtained by the sub-pool of experts with a deep knowledge of the landslides and built environment of the study area have low standard deviation; they are more consistent than the answers obtained by the whole European experts pool, given that they know the typical landslide characteristics in the study area (e.g. landslide velocity, affected material, height of landslide scarps) as well as the characteristics of the built environment that may influence the physical vulnerability (e.g. age, state of conservation, construction materials) better, and are better able to assess the degree of loss produced by the impact of landslides. This shows that the vulnerability is in part a site-specificity parameter, and it has to be taken into account during vulnerability assessment by a questionnaire.

The standard deviation tends to be higher for lower magnitude landslides, for which the potential damage is more difficult to assess than for the higher magnitude landslides, which are considered as highly destructive by the large majority of experts within the sub-pool of experts. Implications of high standard deviation for final risk calculation may be relevant. For example, assessing the risk for a SBT1 building, with a value of EUR 100,000, affected by a landslide with 0.5 m high accumulated material located in the highest landslide susceptibility class, the annual risk is EUR 33.6 considering the average vulnerability. However, the risk may range between EUR 18 and 49 considering the standard deviation value, which means a difference of 46 % to the average value.

If we consider that the sub-pool experts have a more accurate opinion of the building vulnerability to landslides in the Loures municipality, we can state that the pool of European landslide experts overestimated the low-magnitude landslides and underestimated the high-magnitude landslides. Regarding the vulnerability assessment by the European landslide experts, most of them merely completed the questionnaire, but some of them expressed doubts that arose while filling in the questionnaire or made some comments. Whenever necessary, emails were exchanged before the experts completed the questionnaire. Most of the experts who had doubts expressed that it was difficult to assess the potential damage caused by a landslide to a building based only on the depth of the landslide slip surface or the height of accumulated material. Additionally, the structure of the building and its position on the landslide body or foot were referred as major concerns. However, it was not useful to give them more detailed information about the building position or about the characteristics of the landslides (e.g. the velocity of the landslide, the type of affected material, the height of the scarp) as they requested, because such information was not available for the complete landslide inventory and the aim of this study is to assess the vulnerability of the buildings of a whole municipality in a systematic fashion. One adopted solution was to consider the worst case scenario for the potential damage assessment; i.e. the height of the scarp is slightly smaller than the depth of the slip surface; the building is partly within the body and partly outside (on the scarp); the foot is perpendicular to length of the building; and the building is well within the foot, not simply touched by it. This model is quite conservative in that in more favourable situations, damage would logically be lower. But as some of the experts expressed the potential damage as maximum, and the others as medium, the average values provide a model that is not too conservative, but not too low either in terms of expected potential damage, and this is what the authors were seeking.

Regarding the representation of the buildings' vulnerability at the municipal scale, the vulnerability approach based on statistical mapping units is satisfactory. This approach is time-saving and provides correct results when the structural building types within the BGRI subsections are homogeneous. In the BGRI subsections where the structural building types are very heterogeneous, it is useful to take time to identify the structural building type of each building, by fieldwork.

The vulnerability assessment developed in this study has three main advantages: first, the method can be applied to the buildings of the whole Loures municipality despite its huge number (more than 30 000) and the few data available for these buildings; second, the variability of results can be assessed by calculating the standard deviation of the attributed vulnerabilities; third, the vulnerability assessment method developed in this study was applied to the Loures municipality, but it can be reproduced in another municipality or a region with similar landslide types and built environment in a reasonable time.

However, the risk analysis presented here has some limitations and drawbacks involving both the hazard assessment and the potential damage assessment. In relation to the hazard assessment, the spatiotemporal probabilities were overestimated as they were calculated on the landslide areas as a whole. Therefore, the risk calculated for a building constructed on a landslide body on the one hand, or on a landslide foot on the other hand was also amplified because the potential damage was assessed separately for the body and the foot. In addition, the spatiotemporal probabilities were calculated on the basis of the total areas of the inventoried landslides, considering that the 686 landslides of the Loures municipality were the only ones that occurred from 1967 (first landslides inventoried and dated) until 2004 (date of the orthophoto maps used to complete the inventory); in reality, it is obvious that the real total affected area is larger because we could not have inventoried all the landslides that occurred in the Loures municipality during this period. An annual inventory of the whole municipality and extensive fieldwork from 1967 to 2004 could be the solution to obtain a complete landslide inventory. From this point of view, the hazard was underestimated. In addition, changes in the frequency of occurrence of landslides associated with climate change increase the uncertainty of probabilities computed for 10, 25, and 50 years.

In relation to the potential damage assessment, the element at risk values were underestimated. Indeed, the value of the contents inside the buildings was not considered as they were not known. Moreover, indirect costs linked to the function of the building are difficult to quantify and were not considered in this study, although they play an important role in a complete risk analysis. Some examples of these indirect costs would be the costs linked to the temporary or definitive resettling of families whose house has been destroyed by a landslide, as well as the eventual additional costs of transportation if their resettled home is farther from their work place. Another example of indirect costs is the capital lost by the cessation of activity in case an industry or an office were destroyed or damaged by a landslide. Last but not least, it would be even worse if the destroyed building was a strategic building such as a hospital or a school; the vital and sensitive role of these kinds of buildings was not considered in this study, which is another limitation.

The risk analysis is based on the assumption that future landslides will have similar characteristics to the past ones; however, if the landslide preparatory and triggering conditions change (e.g. due to climate change or direct human interference on slopes), the number of landslides and their magnitude would increase, as would the associated damage, and that would have to be considered.

Finally, the risk is underestimated for the scenarios of 10, 25, or 50 years, because it was calculated for the buildings that exist presently, without taking the urban expansion into account, which is a factor of element at risk exposure, and is thus responsible for an increasing risk.

An assessment of buildings' vulnerability to landslides, based on an inquiry of nine magnitude scenarios by a pool and a sub-pool of landslide experts, was developed and applied to Loures, a municipality within the greater Lisbon area. The obtained vulnerabilities vary from 0.2 to 1 as a function of the structural building types and increase with the landslide magnitude, being maximal for a 10 m or a 20 m deep landslide. The annual and multiannual landslide risk has also been computed for the nine magnitude scenarios; the maximum annual risk occurs for the landslides that are 3 m deep, with a maximum value of EUR 25.68 per 5 m pixel.

For the other magnitude scenarios, risk values are low, but they should not be confused with the potential loss values. Indeed, the risk values of the landslides that are 5, 10, or 20 m deep are low because the magnitude probabilities of these landslides are low; nevertheless, when these landslides occur, they produce severe or very severe damages to the buildings.

The analysis of the landslide risk for the buildings of the Loures municipality enables the stakeholders to focus on the buildings for which the landslide vulnerability and the landslide risk are high. All the magnitude scenarios must be taken into account for accurate planning. The landslides that have a low-magnitude being more frequent, the risk they imply has to be considered for short-term planning, whereas the risk implied by high-magnitude landslides has to be considered for long-term planning.

Landslide risk analysis performed in this work may be very useful for insurance companies, which are interested in risk values for buildings, but it may not be so useful for end users dealing with spatial planning and civil protection. Indeed, for spatial planning stakeholders, it is crucial to know where future landslides will occur in order to select the safest zones for development purposes. Therefore, a validated landslide susceptibility assessment, as the one which was presented by Guillard and Zêzere (2012), is a very useful tool for spatial planning, which can be improved with additional data on landslide magnitude and landslide frequency. On the other hand, the civil protection stakeholders need to know the landslide risk for buildings that have a vital or strategic role (e.g. hospitals, schools), but also the location of the population that need to be protected, including the most vulnerable groups of people. Therefore, the landslide hazard assessment and mapping is not enough for civil protection and should be complemented by the assessment of the specific risk (hazard × vulnerability), namely for critical structures and infrastructures, which might be more useful and less time-consuming than the complete risk analysis for the complete built environment.